No, to the best of our knowledge a parking ticket from Ontario would not be placed on your Texas driving record.
Ontario, Canada has reciprocal agreements with many states but these agreements may not include sharing traffic tickets for all motorists. Some agreements may only be for commercial drivers, etc.
The Ontario Ministry of Transportation (MTO) notes that they have reciprocal agreements for posting tickets from the US to a Canadian driving record were with Michigan and New York, a deal may be worked out with Florida soon as well. The Ontario courts or MTO share Ontario traffic tickets with Michigan and New York. A representative for the MTO said they may still inform licensing agencies of other states that were not reciprocal states but she couldn't confirm if it was done regularly for any states other than MI and NY and was highly doubtful it would be done for a non-moving violation such as a parking ticket.
[Let CarInsurance.com help you find affordable auto insurance now.] Even if Texas did have a reciprocal agreement with Ontario, Canada regarding traffic tickets this would normally only be in regards to moving violations. Parking tickets and other non-moving violations do not usually get shared between states even so it would be highly doubtful that Ontario Canada would inform Texas of a parking violation by a car with Texas plates.
States like to keep track of their driver's moving violations since most have either a system in place where if you have too many points or violations of this type your driving privileges will be suspended, revoked, etc. This is to keep bad drivers off the roadways or try to improve drivers by making them take traffic school, driver improvement courses, etc.
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Parking tickets and other non-moving violations do not normally effect one's motor vehicle record if from out of state (and sometimes not even if they are from in state depending upon state laws) since they typically are not thought of as a negligent act and speak to your ability to drive, just your ability to park correctly and legally.
To find out for certain if Ontario will inform Texas about this citation you can contact the court listed on your Canadian parking ticket. If they do say it is going to be reported to TX than you could contact the Texas Department of Public Safety to find out what they would do with the information out this out of country parking ticket. | 
